Implementation of Neural Network Learning with Minimum L1-Norm Criteria in Alpha Stable Distribution

Minimum L₁-norm optimization model has found extensive applications in linear parameter estimations. L₁-norm model is robust in non Gaussian alpha stable distribution error or noise environments, especially for signals that contain sharp transitions or dynamic processes. However, its implementation is more difficult due to discontinuous derivatives, especially compared with the least-squares model. In this paper, a new neural network for solving L₁-norm optimization problems is presented. It has been proved that this neural network is able to converge to the exact solution to a given problem. Implementation of L₁-norm optimization model is presented, where a new neural network is constructed and its performance is evaluated theoretically and experimentally